Curve Analysis

Derivatives

100

3x^2

6x

200

5x^4 + 7x + 6

20x^3 + 7

300

e^5x

5e^5x

400

5cosx - sinx + 30x^5

-5sinx-cos+150x^4

500

9cscx + 14tanx^3 - 4cotx^6 + 3668298279

−9⋅cot(x)⋅csc(x)+42⋅(sec(x))^2⋅(tan(x))^2+24⋅(cot(x))^5⋅ (csc(x))^2

First Derivatives

100

Find the Critical Points of the function: y = −x^3+ 2x^2+ 2

Critical points at: x = 0, 4/3

200

Find the Critical Values of the function: y = x^3 − 11x^2 + 39x − 47

Critical points at: x = 3, 13/3

300

Find where the function: y = −x^4 + 3x^2− 3 is increasing and decreasing

Increasing: (−∞, √3/2) , (0, √3/2) Decreasing: (-√3/2, 0) , (√3/2, ∞)

400

y =3x^2− 3x^3 Find CP, Intervals Increasing/Decreasing, AND Discontinuities (if any).

Critical points at: x = − 3, 3 Discontinuity at: x = 0 Increasing: (− 3, 0), (0, 3) Decreasing: (−∞, − 3), ( 3, ∞)

500

y = −1/5(x − 4)^(5/3)− 2(x − 4)^2/3 − 1 CP, Increasing/Decreasing, Discontinuities (if any)

Critical points at: x = 0, 4 No discontinuities exist. Increasing: (0, 4) Decreasing: (−∞, 0), (4, ∞)

Second Derivatives

100

y = x^3 − 3x^2 + 4

Concave up: (1, ∞) Concave down: (−∞, 1)

200

y = x^3 − 2x^2 − 2

Concave up: (2/3, ∞) Concave down: (−∞,2/3)

300

y = x^4 + x^3 − 3x^2+ 1

Concave up: (−∞, −1), (1/2, ∞) Concave down: (−1,1/2)

400

y = (−x^3)/(x^2 − 4) Concavity AND Point of Inflection

Concave up: (−∞, −2), (0, 2) Concave down: (−2, 0), (2, ∞) Inflection point at: x = 0

500

y = (−3/16)(x − 1)^(4/3) −(3/2)(x − 1)^(1/3) + 2 Concavity AND Point of Inflection

Concave up: (1, 5) Concave down: (−∞, 1), (5, ∞) Inflection points at: x = 1, 5

Mean Value Theorem

100

x^2 - 5x + 7 on the interval [-1,3]

x=1

200

x^3 - 6x^2 + 9x + 2 on the interval [0,4]

x= 3.154700539 and x= .845299461

300

f(x)= x^4 - 16x^2 + 2 on the interval [-1,3] Find the value of c

x = 0.3819660113 and 2.618033989.

400

f(z)= z^3 - 8z^2 + 7z - 2 on the interval [2,5]

(2+√79)/3

500

f(x)=ln(x^2 + 2x + 4) on the interval [-4,3]

x = -0.9012084345

Random

100

Which two people are known as the creators of Calculus?

Isaac Newton Gottfried Leibniz

200

Name 3 of Fetty Wap's songs

Answers include: Trap Queen 679 My Way RGF Island Cake Team (if you know more than what's listed here there's something wrong with you)

300

Which team was the winner of the 1990 NBA finals?

Detroit Pistons

400

Name the 4 most commonly spoken languages in the world in order. (1-4)

1. Chinese 1,197,000,000 2. Spanish 414,000,000 3. English 335,000,000 4. Hindi 260,000,000

500

In which phase of meiosis does crossing over occur?

Prophase I